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The Session was intended to give a broad survey of the mathematical
problems arising in the chaotic transition of deterministic
dynamical systems, both in classical and quantum mechanics.
The lectures of Mather and Forni thoroughly cover the area-
preserving twist maps, and include an up-to-date version of the
Aubry-Mather theory.
The lectures of Bellissard describe the quantum aspects: classical
limit, localization, spectral properties of the relevant
SchrAdinger operators and thus represent an exhaus- tive
introduction to the mathematics of "quantum chaos."
The lectures of Degli Esposti et al. reviews equidistribu- tion of
unstable periodic orbits and classical limit of quantized toral
symplectomorphisms.
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